Area-Preserving Diffeomorphisms, w_\infty Algebras and w_\infty Gravity

Details Area-Preserving Diffeomorphisms, w_\infty Algebras and w_\infty Gravity Area-Preserving Diffeomorphisms, w_\infty Algebras and w_\infty Gravity

1992-02-26

arxiv.org/abs/hep-th/9202086v1

Physics

High Energy Physics

High Energy Physics - Theory

24 pages

Scientific paper

The w_\infty algebra is a particular generalization of the Virasoro algebra with generators of higher spin 2,3,...,\infty. It can be viewed as the algebra of a class of functions, relative to a Poisson bracket, on a suitably chosen surface. Thus, w_\infty is a special case of area-preserving diffeomorphisms of an arbitrary surface. We review various aspects of area- preserving diffeomorphisms, w_\infty algebras and w_\infty gravity. The topics covered include a) the structure of the algebra of area-preserving diffeomorphisms with central extensions and their relation to w_\infty algebras, b) various generalizations of w_\infty algebras, c) the structure of w_\infty gravity and its geometrical aspects, d) nonlinear realizations of w_\infty symmetry and e) various quantum realizations of w_\infty symmetry.

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